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A unit square is drawn. Then an equilateral triangle is constructed on each side of the unit square, and the four new points of the diagram are joined to form a larger square. Find the area of the larger square.

 

 Dec 26, 2019
 #1
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0

Combining the areas of all the regions, I'm getting that the area of the large square is 3 + 2*sqrt(3).

 Dec 26, 2019
 #2
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sry thats not right

Guest Dec 26, 2019
 #3
avatar+106516 
+2

The height, H,  of one of the equilateral triangles   can be found as

 

tan 60   =   H /(1/2)

√3/2  = H

 

The diagonal of the square  =   2H  + 1 =   √3  +  1

 

The side of the larger  square = diagonal / √2  =     [ √3 + 1  ]  / √2

 

So....the area  of the larger square  =  

 

[ √3 + 1 ] ^2 / 2     =    [ 3 + 2√3 + 1' / 2   =  [4 + 2√3 ] / 2   =   [ 2 + √3 ]  units^2  ≈  3.732 units^2 

 

 

cool cool cool

 Dec 26, 2019
 #6
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+1

thx cphill

Guest Dec 26, 2019
 #4
avatar+141 
+2

Smaller square side                  a = 1

Equilateral triangle side             s = 1

Equilateral triangle height         h =  sqrt [ s2 - ( s/2)2 ]       h = sqrt [ 1 - (1/2)2 ]  = 0.866

The area of a larger square      A = 2( h + a/2 )2                 A = 2(0.866+0.5)2  =  3.732 u2  indecision                                      

 Dec 26, 2019
 #5
avatar+106516 
+1

Good job, Dragan   !!!!

 

 

 

cool cool cool

CPhill  Dec 26, 2019
 #7
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+1

thxd dragan

Guest Dec 26, 2019
 #8
avatar+141 
+1

u r w

Dragan  Dec 26, 2019

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